As Tesla Motors Inc. extended its rapid run higher this week, trading in options on the electric car maker saw their busiest week ever as investors scrambled for alternative ways to “short” the stock.

Tesla’s shares have more than doubled in price since the beginning of April to a high of $97.12, putting a squeeze on those who have tried to sell the stock short using borrowed shares.

As of Thursday, about 25% of Tesla free float–or shares publicly owned and available for trading–was on loan to short sellers, according to Markit. That compares with 2.3% of the S&P 500 as a whole.

As a result, investors are turning to the options market to make bets that Tesla has rallied too far, too fast, said Brian Overby, senior options analyst at online brokerage TradeKing.

Investors can also establish a “short” position by buying put options, which secure a selling price through a set date. And as demand for short positions rose this week, so too did prices on put options, Mr. Overby said.

One Friday, a put option with a strike price 10% below the current stock value expiring next week cost about $2, where a put option with a strike price 10% out of the money expiring this session was priced at $1.55 a week ago, according to FactSet data.

The total number of outstanding put options, which grant the right to sell shares at a set price, rose to about 399,000 contracts Friday, up 36% in the first four days of the week, and 92% from the beginning of last week.

“Despite the inflated put prices,” he said, “Traders still flood[ed] to the options market to buy puts.”

Tesla shares added to gains Friday, climbing 22 cents, or 0.2%, to $92.47. The shares exploded higher beginning in the middle of last week, when the electric car company reported its first-ever quarterly profit.

While the number of outstanding bearish bets increased 36% in the first four sessions this week, the number of outstanding bullish bets, or call options, increased by a smaller 25%, according to options-data firm Trade Alert. That led the ratio of bearish options outstanding to bullish ones to rise to 1.8-to-one, from 1.43-to-one at the beginning of last week.

In longer-dated Tesla options, June and December $60 put options saw sharp increases in open interest this week. Those contracts look for Tesla shares to slip back more than 32% through mid-June and mid-December, respectively, to profit.

But in intraday activity, trading in call options, which grant the right to buy shares by a designated date, led, with calls accounting for 58% of trading volume this week.

However, just 8.1% of the trading in call options led to new open interest–or new outstanding contracts. That suggests much of trading in the contracts was investors closing profitable trades, with some new positioning.

In October, when shares traded at about $28 a share, one investor bought about 5,180 January $40 call options at a cost of about $2 a share. Data suggests that an investor exercised his options this week, buying 518,000 shares now worth about $46.6 million for $21.8 million.

The most actively traded Tesla options contracts this week were May $100 and May $95 call options, and May $80 put options, all with more than 31,000 contracts trading in the first four sessions of the week. The call options grant the right to buy shares at $100 or $95 a share, while the puts grant the right to sell at $80. With the stock at $90 at midday Friday, all three look set to expire worthless. May options expire after the close of trading Friday.

About 32% of total contracts outstanding will expire after the close Friday.

Last week, Tesla options trading volume set a new record, with 814,522 contracts traded, according to Trade Alert data. This week’s volume topped that record Thursday, with trading volume reaching more than one million by midafternoon Friday.